Single pixel quantitative phase imaging with spatial frequency projections

We introduce a new single pixel imaging technique that automatically co-registers quantitative phase and incoherent image modalities through the simultaneous acquisition of identical object spatial frequency information. The technique consists of using a time varying groove density diffraction grating to produce a reference and scan beam. The interference between the beams produce time varying spatial frequencies in the sample. The collected light on a single pixel detector produces a time trace that allows easy recovery of coherent and incoherent contrast mechanisms. We derive theory for the quantitative phase and show excellent agreement with experimental data and numeric model. Additionally, we derive a general theory of single pixel quantitative phase theory that can be applied broadly to general methods that use a sequence of modulated light patterns for single pixel phase imaging.